The voltage, $V$, in an electrical outlet is given as a function of time, $t$, by the function $V=T \cos{(a t)}$, where $V$ is in volts and $t$ is in seconds, $T$ is a positive constant representing the maximum voltage, and $a$ is a positive constant related to the frequency of the delivered voltage.

(a)
If $a = 120 \pi$, what is the average value of the voltage over 1 second?
average =

(b)
Engineers do not use the average voltage. They use the root mean square voltage defined by $\overline{V} = \sqrt{\mbox{average of } (V^2)}$. Find $\overline V$ in terms of $T$. (Take the average over $1$ second.)
$\overline{V} =$

(c)
The standard household voltage in parts of Japan is 100 volts, meaning that $\overline{V} = 100$. What is $T$?
$T =$
(In America, the household voltage is 110 volts, at a frequency of 60 Hz, so that $a = 120\pi$.)